Finite Group Databasebeta

← C7×#23878 #13201094

Subgroups — C7×#23878 #13201094

Order 1792.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#575C211yesmaximal, characteristic, complemented
2C7×#3488C211yesmaximal, characteristic, complemented
3C2×C7×#455C211yesmaximal, characteristic, complemented
4C2×C7×#453C211yesmaximal, characteristic, complemented
5C7×#3005C211yesmaximal, characteristic, complemented
6C7×#2431C211yesmaximal, characteristic, complemented
7C7×#2007C211yesmaximal, characteristic, complemented
8C7×#2006C211yesmaximal, characteristic, complemented
9C7×#2004C211yesmaximal, characteristic, complemented
10C7×#2002C211yesmaximal, characteristic, complemented
11C7×#1900C211yesmaximal, characteristic, complemented
12C7×#1883C211yesmaximal, characteristic, complemented
13C7×#1882C211yesmaximal, characteristic, complemented
14C7×#1871C211yesmaximal, characteristic, complemented
15C7×#1789C211yesmaximal, characteristic, complemented
16C2×C7×H(5,𝔽2)C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C22×C7×#41C2211yescharacteristic, complemented
19C7×#575—24no—
20C7×#575—24no—
21C2×C7×#137—21no—
22C2×C7×#137C2211yescharacteristic
23C2×C7×#137C2211yescharacteristic, complemented
24C2×C7×#137C2211yescharacteristic, complemented
25C2×C7×AGL(1,ℤ/8)—21no—
26C2×C7×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C7×AGL(1,ℤ/8)C2211yescharacteristic, complemented
28C2×C7×AGL(1,ℤ/8)C2211yescharacteristic, complemented
29C2×C7×#135—21no—
30C2×C7×#135—21no—
31C22×C7×M16C2211yescharacteristic, complemented
32C7×#550—21no—
33C7×#548—21no—
34C7×#546—21no—
35C7×#546—22no—
36C7×D42—22no—
37C7×D42—21no—
38C7×#537—21no—
39C7×#537C2211yescharacteristic
40C7×#535—21no—
41C7×#535C2211yescharacteristic
42C2×C7×#127C2211yescharacteristic, complemented
43C2×C7×#124C2211yescharacteristic, complemented
44C7×#525—21no—
45C7×#525C2211yescharacteristic
46C2×C7×#121—21no—
47C2×C7×#121C2211yescharacteristic
48C7×#520C2211yescharacteristic
49C7×#455—24no—
50C7×#453—24no—
51C7×#452—21no—
52C7×#452—21no—
53C7×#449—21no—
54C7×#449—21no—
55C2×C7×#104C2211yescharacteristic
56C2×C7×#104C2211yescharacteristic
57C2×C7×#104C2211yescharacteristic, complemented
58C2×C7×#104C2211yescharacteristic, complemented
59C2×C7×#104C2211yescharacteristic, complemented
60C2×C7×#104C2211yescharacteristic, complemented
61C7×#419C2211yescharacteristic, complemented
62C7×#418C2211yescharacteristic, complemented
63C2×C7×#100C2211yescharacteristic, complemented
64C2×C7×#100C2211yescharacteristic, complemented
65C7×#407C2211yescharacteristic, complemented
66C7×#392—22no—
67C7×#391C2211yescharacteristic, complemented
68C7×#390C2211yescharacteristic, complemented
69C7×#386—22no—
70C4×C7×C22⋊C4C2211yescharacteristic, complemented
71C7×#343C2211yescharacteristic, complemented
72C7×#343C2211yescharacteristic, complemented
73C7×#339C2211yescharacteristic, complemented
74C7×#339C2211yescharacteristic, complemented
75#23878C711yesmaximal, characteristic, direct product factor, Sylow
76C7×H(5,𝔽2)—22no—
77C7×H(5,𝔽2)—22no—
78C7×H(5,𝔽2)—41no—
79C7×H(5,𝔽2)—41no—
80C2×C7×#41—21no—
81C2×C7×#41—21no—
82C2×C7×#41—21no—
83C2×C7×#41—21no—
84C2×C7×#41—22no—
85C2×C7×#41—22no—
86C2×C7×#41—22no—
87C2×C7×#41—22no—
88C2×C7×#41—21no—
89C2×C7×#41—21no—
90C2×C7×#41—21no—
91C2×C7×#41—21no—
92C2×C7×#41—41no—
93C2×C7×#41—41no—
94C2×C7×#41—41no—
95C2×C7×#41—41no—
96C2×C7×#41D411yescharacteristic, complemented
97C2×C7×#41D411yescharacteristic, complemented
98C2×C7×#41C2311yescharacteristic
99C2×C7×#41C2311yescharacteristic
100C2×C7×#41C2311yescharacteristic
101C22×C7×Q8D411yescharacteristic, complemented
102C22×C7×Q8C2311yescharacteristic
103C22×C7×D4—21no—
104C22×C7×D4—22no—
105C22×C7×D4—22no—
106C22×C7×D4—21no—
107C22×C7×D4—21no—
108C22×C7×D4—21no—
109C22×C7×D4—22no—
110C22×C7×D4D412yes—
111C22×C7×D4D411yescharacteristic, complemented
112C22×C7×D4C2311yescharacteristic
113C22×C7×D4C2311yescharacteristic
114C23×C4×C7—21no—
115C23×C4×C7—21no—
116C23×C4×C7C2311yescharacteristic
117C7×#137—28no—
118C7×#137—22no—
119C7×#137—22no—
120C7×#137—22no—
121C7×#137—22no—
122C7×#137—41no—
123C7×#137D414yescomplemented
124C7×AGL(1,ℤ/8)—28no—
125C7×AGL(1,ℤ/8)—22no—
126C7×AGL(1,ℤ/8)—22no—
127C7×AGL(1,ℤ/8)—22no—
128C7×AGL(1,ℤ/8)—22no—
129C7×AGL(1,ℤ/8)—41no—
130C7×AGL(1,ℤ/8)D414yescomplemented
131C7×#135—28no—
132C7×#135—28no—
133C2×C7×Q16—21no—
134C2×C7×Q16—21no—
135C2×C7×Q16—21no—
136C2×C7×SD16—21no—
137C2×C7×SD16—21no—
138C2×C7×SD16—21no—
139C2×C7×SD16—21no—
140C2×C7×SD16—21no—
141C2×C7×SD16—21no—
142C2×C7×D8—21no—
143C2×C7×D8—21no—
144C2×C7×D8—21no—
145C2×C7×M16—21no—
146C2×C7×M16—22no—
147C2×C7×M16—22no—
148C2×C7×M16C2311yescharacteristic
149C2×C7×M16C2311yescharacteristic
150C2×C7×M16C2311yescharacteristic
151C2×C7×M16C2311yescharacteristic
152C22×C7×C8—21no—
153C7×#127—22no—
154C7×#127—21no—
155C7×#127—22no—
156C7×#127—41no—
157C7×#124—22no—
158C7×#124—21no—
159C7×#124—22no—
160C7×#124—41no—
161C7×#123—22no—
162C7×#123—21no—
163C7×C22⋊Q8—22no—
164C7×C22⋊Q8—21no—
165C7×C22⋊Q8—21no—
166C7×C22⋊Q8D411yescharacteristic, complemented
167C7×C22⋊Q8D411yescharacteristic, complemented
168C7×#121—22no—
169C7×#121—22no—
170C7×#121—22no—
171C7×#121—22no—
172C7×#121—22no—
173C7×#121—21no—
174C7×#121—21no—
175C7×#121—21no—
176C7×#121—21no—
177C7×#121—21no—
178C7×#121—21no—
179C7×#121—22no—
180C7×#121—21no—
181C7×#121—21no—
182C7×#121D411yescharacteristic, complemented
183C7×#121D411yescharacteristic, complemented
184C7×#120—22no—
185C7×#120—22no—
186C7×#120—22no—
187C7×#120—21no—
188C7×#120—22no—
189C4×C7×Q8—21no—
190C4×C7×D4—22no—
191C4×C7×D4—22no—
192C4×C7×D4—21no—
193C4×C7×D4—22no—
194C4×C7×D4—21no—
195C4×C7×D4—21no—
196C7×#117—21no—
197C7×#117C2311yescharacteristic
198C2×C7×C4⋊C4—21no—
199C2×C7×C4⋊C4C2311yescharacteristic
200C2×C7×C22⋊C4—22no—
201C2×C7×C22⋊C4—21no—
202C2×C7×C22⋊C4—22no—
203C2×C7×C22⋊C4—22no—
204C2×C7×C22⋊C4D412yes—
205C2×C42×C7C2311yescharacteristic
206C2×C42×C7C2311yescharacteristic
207C7×#104—22no—
208C7×#104—22no—
209C7×#104—22no—
210C7×#104—22no—
211C7×#104—41no—
212C7×#104—41no—
213C7×#103—21no—
214C7×#103—21no—
215C7×#102—21no—
216C7×#102—21no—
217C7×#100—22no—
218C7×#100—22no—
219C7×C22⋊C8—21no—
220C7×C22⋊C8—21no—
221C7×#95—21no—
222C7×#95—22no—
223C2×#575C2×C711yescharacteristic, complemented
224#3488C2×C711yescharacteristic, complemented
225C2×#455C2×C711yescharacteristic, complemented
226C2×#453C2×C711yescharacteristic, complemented
227#3005C2×C711yescharacteristic, complemented
228#2431C2×C711yescharacteristic, complemented
229#2007C2×C711yescharacteristic, complemented
230#2006C2×C711yescharacteristic, complemented
231#2004C2×C711yescharacteristic, complemented
232#2002C2×C711yescharacteristic, complemented
233#1900C2×C711yescharacteristic, complemented
234#1883C2×C711yescharacteristic, complemented
235#1882C2×C711yescharacteristic, complemented
236#1871C2×C711yescharacteristic, complemented
237#1789C2×C711yescharacteristic, complemented
238C24×C7—22no—
239C24×C7—21no—
240C24×C7—21no—
241C24×C7C2×D412yes—
242C24×C7C2×D411yescharacteristic
243C7×#41—21no—
244C7×#41—21no—
245C7×#41—24no—
246C7×#41—24no—
247C7×#41—22no—
248C7×#41—22no—
249C7×#41—21no—
250C7×#41—21no—
251C7×#41—21no—
252C7×#41—21no—
253C7×#41—21no—
254C7×#41—21no—
255C7×#41—21no—
256C7×#41—21no—
257C7×#41—42no—
258C7×#41—42no—
259C7×#41—41no—
260C7×#41—41no—
261C7×#41—42no—
262C7×#41—42no—
263C7×#41—42no—
264C7×#41—42no—
265C7×#41—42no—
266C7×#41—42no—
267C7×#41—42no—
268C7×#41—42no—
269C7×#41—42no—
270C7×#41—42no—
271C7×#41—42no—
272C7×#41—42no—
273C7×#41C2×D412yes—
274C7×#41C2×D412yes—
275C2×C7×Q8—21no—
276C2×C7×Q8—21no—
277C2×C7×Q8—22no—
278C2×C7×Q8—21no—
279C2×C7×Q8—21no—
280C2×C7×Q8—21no—
281C2×C7×Q8—21no—
282C2×C7×Q8—41no—
283C2×C7×Q8C2×D411yescharacteristic
284C2×C7×Q8C2×D411yescharacteristic
285C2×C7×Q8C2×D411yescharacteristic
286C2×C7×Q8C2×D412yescomplemented
287C2×C7×D4—21no—
288C2×C7×D4—22no—
289C2×C7×D4—22no—
290C2×C7×D4—22no—
291C2×C7×D4—22no—
292C2×C7×D4—21no—
293C2×C7×D4—21no—
294C2×C7×D4—21no—
295C2×C7×D4—21no—
296C2×C7×D4—21no—
297C2×C7×D4—22no—
298C2×C7×D4—22no—
299C2×C7×D4—22no—
300C2×C7×D4—21no—
301C2×C7×D4—22no—
302C2×C7×D4—21no—
303C2×C7×D4—21no—
304C2×C7×D4—21no—
305C2×C7×D4—21no—
306C2×C7×D4—21no—
307C2×C7×D4—21no—
308C2×C7×D4—21no—
309C2×C7×D4—21no—
310C2×C7×D4—21no—
311C2×C7×D4—21no—
312C2×C7×D4—21no—
313C2×C7×D4—21no—
314C2×C7×D4—41no—
315C2×C7×D4—42no—
316C2×C7×D4—42no—
317C2×C7×D4—42no—
318C2×C7×D4—44no—
319C2×C7×D4—42no—
320C2×C7×D4—42no—
321C2×C7×D4—44no—
322C2×C7×D4—44no—
323C2×C7×D4—42no—
324C2×C7×D4—42no—
325C2×C7×D4—41no—
326C2×C7×D4—41no—
327C2×C7×D4—42no—
328C2×C7×D4—44no—
329C2×C7×D4—82no—
330C2×C7×D4—82no—
331C2×C7×D4—84no—
332C2×C7×D4C2×D411yescharacteristic
333C2×C7×D4C2×D411yescharacteristic
334C2×C7×D4C2×D411yescharacteristic
335C2×C7×D4C2×D412yescomplemented
336C22×C4×C7—21no—
337C22×C4×C7—21no—
338C22×C4×C7—21no—
339C22×C4×C7—21no—
340C22×C4×C7—21no—
341C22×C4×C7—22no—
342C22×C4×C7—21no—
343C22×C4×C7—21no—
344C22×C4×C7—21no—
345C22×C4×C7—22no—
346C22×C4×C7—21no—
347C22×C4×C7—21no—
348C22×C4×C7—21no—
349C22×C4×C7—21no—
350C22×C4×C7—21no—
351C22×C4×C7—42no—
352C22×C4×C7—42no—
353C22×C4×C7—42no—
354C22×C4×C7—42no—
355C22×C4×C7—41no—
356C22×C4×C7—41no—
357C22×C4×C7C2×D411yescharacteristic
358C22×C4×C7C2×D411yescharacteristic
359C22×C4×C7C2×D411yescharacteristic
360C22×C4×C7C2×D411yescharacteristic
361C22×C4×C7C2×D411yescharacteristic
362C22×C4×C7C2×D412yes—
363C22×C4×C7C2411yescharacteristic
364C7×Q16—24no—
365C7×Q16—24no—
366C7×Q16—42no—
367C7×SD16—24no—
368C7×SD16—24no—
369C7×SD16—24no—
370C7×SD16—24no—
371C7×SD16—42no—
372C7×SD16—42no—
373C7×D8—24no—
374C7×D8—24no—
375C7×D8—42no—
376C7×M16—24no—
377C7×M16—21no—
378C7×M16—21no—
379C7×M16—21no—
380C7×M16—21no—
381C7×M16—21no—
382C7×M16—21no—
383C7×M16C2×D412yescomplemented
384C7×M16C2×D412yescomplemented
385C2×C7×C8—24no—
386C2×C7×C8—21no—
387C2×C7×C8—21no—
388C2×C7×C8—21no—
389C2×C7×C8—21no—
390C7×C4⋊C4—22no—
391C7×C4⋊C4—22no—
392C7×C4⋊C4—21no—
393C7×C4⋊C4—21no—
394C7×C4⋊C4—21no—
395C7×C4⋊C4—21no—
396C7×C4⋊C4C2×D411yescharacteristic
397C7×C4⋊C4C2×D411yescharacteristic
398C7×C22⋊C4—22no—
399C7×C22⋊C4—22no—
400C7×C22⋊C4—22no—
401C7×C22⋊C4—22no—
402C7×C22⋊C4—22no—
403C7×C22⋊C4—21no—
404C7×C22⋊C4—21no—
405C7×C22⋊C4—21no—
406C7×C22⋊C4—21no—
407C7×C22⋊C4—22no—
408C7×C22⋊C4—22no—
409C7×C22⋊C4—21no—
410C7×C22⋊C4—44no—
411C7×C22⋊C4—42no—
412C7×C22⋊C4—82no—
413C42×C7—22no—
414C42×C7—21no—
415C42×C7—21no—
416C42×C7—21no—
417C42×C7—21no—
418C42×C7—21no—
419C2×H(5,𝔽2)C22×C711yescharacteristic
420C22×#41C22×C711yescharacteristic
421C22×#41C22×C711yescharacteristic, complemented
422#575—24no—
423#575—24no—
424C2×#137—21no—
425C2×#137C22×C711yescharacteristic
426C2×#137C22×C711yescharacteristic, complemented
427C2×#137C22×C711yescharacteristic, complemented
428C2×AGL(1,ℤ/8)—21no—
429C2×AGL(1,ℤ/8)C22×C711yescharacteristic
430C2×AGL(1,ℤ/8)C22×C711yescharacteristic, complemented
431C2×AGL(1,ℤ/8)C22×C711yescharacteristic, complemented
432C2×#135—21no—
433C2×#135—21no—
434C22×M16C22×C711yescharacteristic, complemented
435#550—21no—
436#548—21no—
437#546—21no—
438#546—22no—
439D42—22no—
440D42—21no—
441#537—21no—
442#537C22×C711yescharacteristic
443#535—21no—
444#535C22×C711yescharacteristic
445C2×#127C22×C711yescharacteristic, complemented
446C2×#124C22×C711yescharacteristic, complemented
447#525—21no—
448#525C22×C711yescharacteristic
449C2×#121—21no—
450C2×#121C22×C711yescharacteristic
451#520C22×C711yescharacteristic
452#455—24no—
453#453—24no—
454#452—21no—
455#452—21no—
456#449—21no—
457#449—21no—
458C2×#104C22×C711yescharacteristic
459C2×#104C22×C711yescharacteristic
460C2×#104C22×C711yescharacteristic, complemented
461C2×#104C22×C711yescharacteristic, complemented
462C2×#104C22×C711yescharacteristic, complemented
463C2×#104C22×C711yescharacteristic, complemented
464#419C22×C711yescharacteristic, complemented
465#418C22×C711yescharacteristic, complemented
466C2×#100C22×C711yescharacteristic, complemented
467C2×#100C22×C711yescharacteristic, complemented
468#407C22×C711yescharacteristic, complemented
469#392—22no—
470#391C22×C711yescharacteristic, complemented
471#390C22×C711yescharacteristic, complemented
472#386—22no—
473C4×C22⋊C4C22×C711yescharacteristic, complemented
474#343C22×C711yescharacteristic, complemented
475#343C22×C711yescharacteristic, complemented
476#339C22×C711yescharacteristic, complemented
477#339C22×C711yescharacteristic, complemented
478C23×C7—21no—
479C23×C7—21no—
480C23×C7—21no—
481C23×C7—22no—
482C23×C7—21no—
483C23×C7—21no—
484C23×C7—22no—
485C23×C7—22no—
486C23×C7—22no—
487C23×C7—41no—
488C23×C7—41no—
489C23×C7—42no—
490C23×C7—42no—
491C23×C7—42no—
492C23×C7—42no—
493C23×C7—44no—
494C23×C7—42no—
495C23×C7—42no—
496C23×C7—41no—
497C23×C7—41no—
498C23×C7—81no—
499C23×C7—82no—
500C23×C7—82no—
501C23×C7#12011yescharacteristic
502C23×C7#12011yescharacteristic
503C23×C7C22×D411yescharacteristic
504C7×Q8—21no—
505C7×Q8—21no—
506C7×Q8—22no—
507C7×Q8—21no—
508C7×Q8—21no—
509C7×Q8—22no—
510C7×Q8—21no—
511C7×Q8—42no—
512C7×Q8—41no—
513C7×Q8—41no—
514C7×Q8#12012yes—
515C7×D4—22no—
516C7×D4—22no—
517C7×D4—21no—
518C7×D4—22no—
519C7×D4—21no—
520C7×D4—21no—
521C7×D4—21no—
522C7×D4—22no—
523C7×D4—21no—
524C7×D4—42no—
525C7×D4—42no—
526C7×D4—44no—
527C7×D4—42no—
528C7×D4—44no—
529C7×D4—44no—
530C7×D4—42no—
531C7×D4—44no—
532C7×D4—44no—
533C7×D4—41no—
534C7×D4—41no—
535C7×D4—41no—
536C7×D4—41no—
537C7×D4—41no—
538C7×D4—41no—
539C7×D4—41no—
540C7×D4—41no—
541C7×D4—41no—
542C7×D4—41no—
543C7×D4—81no—
544C7×D4—82no—
545C7×D4—82no—
546C7×D4—82no—
547C7×D4—82no—
548C7×D4—88no—
549C7×D4#12012yes—
550C2×C4×C7—21no—
551C2×C4×C7—21no—
552C2×C4×C7—21no—
553C2×C4×C7—21no—
554C2×C4×C7—21no—
555C2×C4×C7—21no—
556C2×C4×C7—21no—
557C2×C4×C7—21no—
558C2×C4×C7—21no—
559C2×C4×C7—21no—
560C2×C4×C7—21no—
561C2×C4×C7—22no—
562C2×C4×C7—22no—
563C2×C4×C7—22no—
564C2×C4×C7—21no—
565C2×C4×C7—22no—
566C2×C4×C7—21no—
567C2×C4×C7—21no—
568C2×C4×C7—21no—
569C2×C4×C7—22no—
570C2×C4×C7—42no—
571C2×C4×C7—42no—
572C2×C4×C7—42no—
573C2×C4×C7—44no—
574C2×C4×C7—44no—
575C2×C4×C7—44no—
576C2×C4×C7—41no—
577C2×C4×C7—41no—
578C2×C4×C7—41no—
579C2×C4×C7—41no—
580C2×C4×C7—41no—
581C2×C4×C7—41no—
582C2×C4×C7—41no—
583C2×C4×C7—41no—
584C2×C4×C7—42no—
585C2×C4×C7—41no—
586C2×C4×C7—41no—
587C2×C4×C7—41no—
588C2×C4×C7—82no—
589C2×C4×C7#12011yescharacteristic
590C2×C4×C7#12011yescharacteristic
591C2×C4×C7C22×D411yescharacteristic
592C2×C4×C7C22×D411yescharacteristic
593C2×C4×C7C22×D411yescharacteristic
594C2×C4×C7C22×D411yescharacteristic
595C2×C4×C7H(5,𝔽2)11yescharacteristic
596C2×C4×C7H(5,𝔽2)11yescharacteristic
597C7×C8—22no—
598C7×C8—22no—
599C7×C8—41no—
600C7×C8—41no—
601H(5,𝔽2)—22no—
602H(5,𝔽2)—22no—
603H(5,𝔽2)—41no—
604H(5,𝔽2)—41no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—22no—
610C2×#41—22no—
611C2×#41—22no—
612C2×#41—22no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41—21no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41—41no—
620C2×#41—41no—
621C2×#41C7×D411yescharacteristic, complemented
622C2×#41C7×D411yescharacteristic, complemented
623C2×#41C23×C711yescharacteristic
624C2×#41C23×C711yescharacteristic
625C2×#41C23×C711yescharacteristic
626C22×Q8C7×D411yescharacteristic, complemented
627C22×Q8C23×C711yescharacteristic
628C22×D4—21no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—21no—
634C22×D4—22no—
635C22×D4C7×D412yes—
636C22×D4C7×D411yescharacteristic, complemented
637C22×D4C23×C711yescharacteristic
638C22×D4C23×C711yescharacteristic
639C23×C4—21no—
640C23×C4—21no—
641C23×C4C23×C711yescharacteristic
642#137—28no—
643#137—22no—
644#137—22no—
645#137—22no—
646#137—22no—
647#137—41no—
648#137C7×D414yescomplemented
649AGL(1,ℤ/8)—28no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—22no—
652AGL(1,ℤ/8)—22no—
653AGL(1,ℤ/8)—22no—
654AGL(1,ℤ/8)—41no—
655AGL(1,ℤ/8)C7×D414yescomplemented
656#135—28no—
657#135—28no—
658C2×Q16—21no—
659C2×Q16—21no—
660C2×Q16—21no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×SD16—21no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×D8—21no—
668C2×D8—21no—
669C2×D8—21no—
670C2×M16—21no—
671C2×M16—22no—
672C2×M16—22no—
673C2×M16C23×C711yescharacteristic
674C2×M16C23×C711yescharacteristic
675C2×M16C23×C711yescharacteristic
676C2×M16C23×C711yescharacteristic
677C22×C8—21no—
678#127—22no—
679#127—21no—
680#127—22no—
681#127—41no—
682#124—22no—
683#124—21no—
684#124—22no—
685#124—41no—
686#123—22no—
687#123—21no—
688C22⋊Q8—22no—
689C22⋊Q8—21no—
690C22⋊Q8—21no—
691C22⋊Q8C7×D411yescharacteristic, complemented
692C22⋊Q8C7×D411yescharacteristic, complemented
693#121—22no—
694#121—22no—
695#121—22no—
696#121—22no—
697#121—22no—
698#121—21no—
699#121—21no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—22no—
705#121—21no—
706#121—21no—
707#121C7×D411yescharacteristic, complemented
708#121C7×D411yescharacteristic, complemented
709#120—22no—
710#120—22no—
711#120—22no—
712#120—21no—
713#120—22no—
714C4×Q8—21no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—22no—
719C4×D4—21no—
720C4×D4—21no—
721#117—21no—
722#117C23×C711yescharacteristic
723C2×C4⋊C4—21no—
724C2×C4⋊C4C23×C711yescharacteristic
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4C7×D412yes—
730C2×C42C23×C711yescharacteristic
731C2×C42C23×C711yescharacteristic
732#104—22no—
733#104—22no—
734#104—22no—
735#104—22no—
736#104—41no—
737#104—41no—
738#103—21no—
739#103—21no—
740#102—21no—
741#102—21no—
742#100—22no—
743#100—22no—
744C22⋊C8—21no—
745C22⋊C8—21no—
746#95—21no—
747#95—22no—
748C22×C7—21no—
749C22×C7—21no—
750C22×C7—21no—
751C22×C7—21no—
752C22×C7—22no—
753C22×C7—21no—
754C22×C7—21no—
755C22×C7—21no—
756C22×C7—21no—
757C22×C7—44no—
758C22×C7—41no—
759C22×C7—41no—
760C22×C7—41no—
761C22×C7—42no—
762C22×C7—41no—
763C22×C7—42no—
764C22×C7—41no—
765C22×C7—42no—
766C22×C7—41no—
767C22×C7—42no—
768C22×C7—41no—
769C22×C7—41no—
770C22×C7—81no—
771C22×C7—81no—
772C22×C7—82no—
773C22×C7—82no—
774C22×C7—82no—
775C22×C7—84no—
776C22×C7—81no—
777C22×C7—81no—
778C22×C7—164no—
779C22×C7C2×#12011yescharacteristic
780C22×C7D4211yescharacteristic
781C22×C7D4211yescharacteristic
782C4×C7—21no—
783C4×C7—21no—
784C4×C7—22no—
785C4×C7—42no—
786C4×C7—41no—
787C4×C7—41no—
788C4×C7—42no—
789C4×C7—41no—
790C4×C7—42no—
791C4×C7—41no—
792C4×C7—81no—
793C4×C7C2×#12011yescharacteristic
794C4×C7#53411yescharacteristic
795C4×C7D4211yescharacteristic
796C4×C7D4211yescharacteristic
797C24—22no—
798C24—21no—
799C24—21no—
800C24C2×C7×D412yes—
801C24C2×C7×D411yescharacteristic
802#41—21no—
803#41—21no—
804#41—24no—
805#41—24no—
806#41—22no—
807#41—22no—
808#41—21no—
809#41—21no—
810#41—21no—
811#41—21no—
812#41—21no—
813#41—21no—
814#41—21no—
815#41—21no—
816#41—42no—
817#41—42no—
818#41—41no—
819#41—41no—
820#41—42no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41—42no—
827#41—42no—
828#41—42no—
829#41—42no—
830#41—42no—
831#41—42no—
832#41C2×C7×D412yes—
833#41C2×C7×D412yes—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—22no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—41no—
842C2×Q8C2×C7×D411yescharacteristic
843C2×Q8C2×C7×D411yescharacteristic
844C2×Q8C2×C7×D411yescharacteristic
845C2×Q8C2×C7×D412yescomplemented
846C2×D4—21no—
847C2×D4—22no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—21no—
860C2×D4—22no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—41no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—44no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—42no—
887C2×D4—44no—
888C2×D4—82no—
889C2×D4—82no—
890C2×D4—84no—
891C2×D4C2×C7×D411yescharacteristic
892C2×D4C2×C7×D411yescharacteristic
893C2×D4C2×C7×D411yescharacteristic
894C2×D4C2×C7×D412yescomplemented
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—22no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—22no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4C2×C7×D411yescharacteristic
917C22×C4C2×C7×D411yescharacteristic
918C22×C4C2×C7×D411yescharacteristic
919C22×C4C2×C7×D411yescharacteristic
920C22×C4C2×C7×D411yescharacteristic
921C22×C4C2×C7×D412yes—
922C22×C4C24×C711yescharacteristic
923Q16—24no—
924Q16—24no—
925Q16—42no—
926SD16—24no—
927SD16—24no—
928SD16—24no—
929SD16—24no—
930SD16—42no—
931SD16—42no—
932D8—24no—
933D8—24no—
934D8—42no—
935M16—24no—
936M16—21no—
937M16—21no—
938M16—21no—
939M16—21no—
940M16—21no—
941M16—21no—
942M16C2×C7×D412yescomplemented
943M16C2×C7×D412yescomplemented
944C2×C8—24no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4C2×C7×D411yescharacteristic
956C4⋊C4C2×C7×D411yescharacteristic
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—21no—
963C22⋊C4—21no—
964C22⋊C4—21no—
965C22⋊C4—21no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—21no—
969C22⋊C4—44no—
970C22⋊C4—42no—
971C22⋊C4—82no—
972C42—22no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C2×C7—21no—
979C2×C7—21no—
980C2×C7—41no—
981C2×C7—41no—
982C2×C7—42no—
983C2×C7—82no—
984C2×C7—81no—
985C2×C7—82no—
986C2×C7—81no—
987C2×C7#240311yescharacteristic
988C2×C7#301811yescharacteristic
989C2×C7#301911yescharacteristic
990C23—21no—
991C23—21no—
992C23—21no—
993C23—22no—
994C23—21no—
995C23—21no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—41no—
1000C23—41no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—44no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
1009C23—41no—
1010C23—81no—
1011C23—82no—
1012C23—82no—
1013C23C7×#12011yescharacteristic
1014C23C7×#12011yescharacteristic
1015C23C22×C7×D411yescharacteristic
1016Q8—21no—
1017Q8—21no—
1018Q8—22no—
1019Q8—21no—
1020Q8—21no—
1021Q8—22no—
1022Q8—21no—
1023Q8—42no—
1024Q8—41no—
1025Q8—41no—
1026Q8C7×#12012yes—
1027D4—22no—
1028D4—22no—
1029D4—21no—
1030D4—22no—
1031D4—21no—
1032D4—21no—
1033D4—21no—
1034D4—22no—
1035D4—21no—
1036D4—42no—
1037D4—42no—
1038D4—44no—
1039D4—42no—
1040D4—44no—
1041D4—44no—
1042D4—42no—
1043D4—44no—
1044D4—44no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—81no—
1056D4—82no—
1057D4—82no—
1058D4—82no—
1059D4—82no—
1060D4—88no—
1061D4C7×#12012yes—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—42no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—44no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—42no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—82no—
1101C2×C4C7×#12011yescharacteristic
1102C2×C4C7×#12011yescharacteristic
1103C2×C4C22×C7×D411yescharacteristic
1104C2×C4C22×C7×D411yescharacteristic
1105C2×C4C22×C7×D411yescharacteristic
1106C2×C4C22×C7×D411yescharacteristic
1107C2×C4C7×H(5,𝔽2)11yescharacteristic
1108C2×C4C7×H(5,𝔽2)11yescharacteristic
1109C8—22no—
1110C8—22no—
1111C8—41no—
1112C8—41no—
1113C7#2387811yescharacteristic, direct product factor, Sylow
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—22no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—44no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—42no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—41no—
1136C22—81no—
1137C22—81no—
1138C22—82no—
1139C22—82no—
1140C22—82no—
1141C22—84no—
1142C22—81no—
1143C22—81no—
1144C22—164no—
1145C22C2×C7×#12011yescharacteristic
1146C22C7×D4211yescharacteristic
1147C22C7×D4211yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—42no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—42no—
1157C4—41no—
1158C4—81no—
1159C4C2×C7×#12011yescharacteristic
1160C4C7×#53411yescharacteristic
1161C4C7×D4211yescharacteristic
1162C4C7×D4211yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—82no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2C7×#240311yescharacteristic
1173C2C7×#301811yescharacteristic
1174C2C7×#301911yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C7×#575C2semidirect
2. C7×#3488C2semidirect
3. C2×C7×#455C2semidirect
4. C2×C7×#453C2semidirect
5. C7×#3005C2semidirect
6. C7×#2431C2semidirect
7. C7×#2007C2semidirect
8. C7×#2006C2semidirect
9. C7×#2004C2semidirect
10. C7×#2002C2semidirect
11. C7×#1900C2semidirect
12. C7×#1883C2semidirect
13. C7×#1882C2semidirect
14. C7×#1871C2semidirect
15. C7×#1789C2semidirect
18. C22×C7×#41C22semidirect
23. C2×C7×#137C22semidirect
24. C2×C7×#137C22semidirect
27. C2×C7×AGL(1,ℤ/8)C22semidirect
28. C2×C7×AGL(1,ℤ/8)C22semidirect
31. C22×C7×M16C22semidirect
42. C2×C7×#127C22semidirect
43. C2×C7×#124C22semidirect
57. C2×C7×#104C22semidirect
58. C2×C7×#104C22semidirect
59. C2×C7×#104C22semidirect
60. C2×C7×#104C22semidirect
61. C7×#419C22semidirect
62. C7×#418C22semidirect
63. C2×C7×#100C22semidirect
64. C2×C7×#100C22semidirect
65. C7×#407C22semidirect
67. C7×#391C22semidirect
68. C7×#390C22semidirect
70. C4×C7×C22⋊C4C22semidirect
71. C7×#343C22semidirect
72. C7×#343C22semidirect
73. C7×#339C22semidirect
74. C7×#339C22semidirect
75. #23878C7direct (N × H)
96. C2×C7×#41D4semidirect
97. C2×C7×#41D4semidirect
101. C22×C7×Q8D4semidirect
111. C22×C7×D4D4semidirect
123. C7×#137D4semidirect
130. C7×AGL(1,ℤ/8)D4semidirect
166. C7×C22⋊Q8D4semidirect
167. C7×C22⋊Q8D4semidirect
182. C7×#121D4semidirect
183. C7×#121D4semidirect
223. C2×#575C2×C7semidirect
224. #3488C2×C7semidirect
225. C2×#455C2×C7semidirect
226. C2×#453C2×C7semidirect
227. #3005C2×C7semidirect
228. #2431C2×C7semidirect
229. #2007C2×C7semidirect
230. #2006C2×C7semidirect
231. #2004C2×C7semidirect
232. #2002C2×C7semidirect
233. #1900C2×C7semidirect
234. #1883C2×C7semidirect
235. #1882C2×C7semidirect
236. #1871C2×C7semidirect
237. #1789C2×C7semidirect
286. C2×C7×Q8C2×D4semidirect
335. C2×C7×D4C2×D4semidirect
383. C7×M16C2×D4semidirect
384. C7×M16C2×D4semidirect
421. C22×#41C22×C7semidirect
426. C2×#137C22×C7semidirect
427. C2×#137C22×C7semidirect
430. C2×AGL(1,ℤ/8)C22×C7semidirect
431. C2×AGL(1,ℤ/8)C22×C7semidirect
434. C22×M16C22×C7semidirect
445. C2×#127C22×C7semidirect
446. C2×#124C22×C7semidirect
460. C2×#104C22×C7semidirect
461. C2×#104C22×C7semidirect
462. C2×#104C22×C7semidirect
463. C2×#104C22×C7semidirect
464. #419C22×C7semidirect
465. #418C22×C7semidirect
466. C2×#100C22×C7semidirect
467. C2×#100C22×C7semidirect
468. #407C22×C7semidirect
470. #391C22×C7semidirect
471. #390C22×C7semidirect
473. C4×C22⋊C4C22×C7semidirect
474. #343C22×C7semidirect
475. #343C22×C7semidirect
476. #339C22×C7semidirect
477. #339C22×C7semidirect
621. C2×#41C7×D4semidirect
622. C2×#41C7×D4semidirect
626. C22×Q8C7×D4semidirect
636. C22×D4C7×D4semidirect
648. #137C7×D4semidirect
655. AGL(1,ℤ/8)C7×D4semidirect
691. C22⋊Q8C7×D4semidirect
692. C22⋊Q8C7×D4semidirect
707. #121C7×D4semidirect
708. #121C7×D4semidirect
845. C2×Q8C2×C7×D4semidirect
894. C2×D4C2×C7×D4semidirect
942. M16C2×C7×D4semidirect
943. M16C2×C7×D4semidirect
1113. C7#23878direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C7×#5752
C7×#34882
C2×C7×#4552
C2×C7×#4532
C7×#30052
C7×#24312
C7×#20072
C7×#20062
C7×#20042
C7×#20022
C7×#19002
C7×#18832
C7×#18822
C7×#18712
C7×#17892
#238787